Problem: You are given an unweighted tree with n vertices. Recall that a tree is a connected undirected graph without cycles.

Your task is to choose three distinct vertices a, b, c on this tree such that the number of edges which belong to at least one of the simple paths between a and b, b and c, or a and c is the maximum possible. See the notes section for a better understanding.

The simple path is the path that visits each vertex at most once.

Input

The first line contains one integer number n (3 ≤ n ≤ 2 ⋅ 10^5) — the number of vertices in the tree. 

Next n - 1 lines describe the edges of the tree in form a_i, b_i (1 ≤ a_i, b_i ≤ n, a_i ≠ b_i). It is guaranteed that given graph is a tree.

Output

In the first line print one integer res — the maximum number of edges which belong to at least one of the simple paths between a and b, b and c, or a and c.

In the second line print three integers a, b, c such that 1 ≤ a, b, c ≤ n and a ≠, b ≠ c, a ≠ c.

If there are several answers, you can print any.

Example

Input


8
1 2
2 3
3 4
4 5
4 6
3 7
3 8


Output


5
1 8 6

Note

The picture corresponding to the first example (and another one correct answer):

<image>

If you choose vertices 1, 5, 6 then the path between 1 and 5 consists of edges (1, 2), (2, 3), (3, 4), (4, 5), the path between 1 and 6 consists of edges (1, 2), (2, 3), (3, 4), (4, 6) and the path between 5 and 6 consists of edges (4, 5), (4, 6). The union of these paths is (1, 2), (2, 3), (3, 4), (4, 5), (4, 6) so the answer is 5. It can be shown that there is no better answer.

Solution (in PYTHON3):

Solution:
import sys
input = sys.stdin.readline
import math
import copy
import collections
from collections import deque

def bfs(vert):
    global adj,visited
    q = deque()
    q.append([vert,0])
    while q:
        temp,dist = q.popleft()
        visited.add(temp)
        for edge in adj[temp]:
            if edge not in visited:
                q.append([edge,dist+1])
        if not q:
            return [temp,dist]

def findpath(a,b):
    global path,adj,visited
    q = deque()
    q.append(a)
    firsts = []
    while q:
        temp = q.pop()
        path.append(temp)
        visited.add(temp)
        if temp==b:
            return
        leaf = True
        first = -1
        for edge in adj[temp]:
            if edge not in visited:
                if leaf:
                    first = edge
                leaf = False
                q.append(edge)
        if first!=-1:
            firsts.append(first)
        if leaf:
            remove = path.pop()
            while remove == firsts[-1]:
                firsts.pop()
                remove = path.pop()

def bfs2(path):
    global visited
    c = -1
    farthest = -1
    for node in path[1:len(path)-1]:
        temp,dist = bfs(node)
        if dist>farthest:
            farthest = dist
            c = temp
    return [c,farthest]

n = int(input())
adj = dict()
for i in range(n-1):
    u,v = map(int,input().split())
    if u not in adj:
        adj[u] = set()
    if v not in adj:
        adj[v] = set()
    adj[v].add(u)
    adj[u].add(v)
visited = set()
a,_ = bfs(1)
visited = set()
b,_ = bfs(a)
path = []
visited = set()
findpath(a,b)
visited = set(path)
c,dist = bfs2(path)
print(len(path)-1+dist)
print(a,b,c)
# visited = set()
# path = []
# findpath(1,15)
# print(path)